The heightened research activity in the interdisciplinary field of network science can be attributed to the emergence of the social network computer applications. Researchers understood early on that data describing how entities interconnect is highly valuable and that it offers a deeper understanding about the entities themselves. This is why there were so many studies done about various kinds of networks in the last 10-15 years. The study of the networks from the perspective of computer science usually has two objectives. The first objective is to develop statistical mechanisms capable of accurately describing and modeling observed real-world networks. A good fit of such mechanism suggests the correctness of the model's assumptions and leads to better understanding of the network. A second goal is more practical, a well performing model can be used to predict what will happen to the network in the future. Also, such model can be leveraged to use the information gleaned from network to predict what will happen to the networks entities. One important leitmotif of network research and analysis is wide adaptation of log linear models. In this work we apply this philosophy for study and evaluation of log-linear statistical models in various types of networks. We begin with proposal of the new Temporal Exponential Random Graph Model (tERGM) for the analysis and predictions in the binary temporal social networks. We then extended the model for applications in partially observed networks that change over time. Lastly, we generalize the tERGM model to predict the real-valued weighted links in the temporal non-social networks. The log-linear models are not limited to networks that change over time but can also be applied to networks that are static. One such static network is a social network composed of patients undergoing hemodialysis. Hemodialysis is prescribed to people suffering from the end stage renal disease; the treatment necessitates the attendance, on non-changing schedule, of the hemodialysis clinic for a prolonged time period and this is how the social ties are formed. The new log-linear Social Latent Vectors (SLV) model was applied to study such static social networks. The results obtained from SLV experiments suggest that social relationships formed by patients bear influence on individual patients clinical outcome. The study demonstrates how social network analysis can be applied to better understand the network constituents. / Computer and Information Science

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Esse trabalho visa a investigar a estrutura bi-Hamiltoniana de uma classe de sistemas dinâmicos. Depois de introduzir as ferramentas necessárias, a saber, as noções de variedade de Poisson, de grupo de PoissonLieedenetworknodiscoenoanêl,introduziremosossistemasdinâmicos relevantes nessa dissertação, chamados de reticulados de Coxeter-Toda. Esses sistemas dinâmicos, cujo espaço de fase pode ser identicado com umoportunoquocientedeumacéluladupladeCoxeter-Bruhatdogrupo linear geral, são obtidos por redução do sistema de Toda em GLn. Na parte nal do presente trabalho apresentaremos alguns resultados relacionado à um sistema dinâmico discreto chamado de aplicação do pentagrama, o qual pode ser obtido através uma oportuna discretização do sistema dinâmico de Boussinesq. / This work aims to study the bi-Hamiltonian structure of a class of dynamical systems. After introducing the relevant tools, namely the notions of Poisson manifold, Poisson-Lie group and of network dened in a disc and in an annulus, we will introduce the dynamical systems of interest for this dissertation, i.e., the Coxeter-Toda lattices. These dynamical systems, whose phase-space can be identied with a suitable quotient of a Coxeter double Bruhat cell of the general linear group, are obtained by reduction starting from the Toda ow on GLn. In the nal part of the present work will be presented some results concerning a discrete integrable system close to the so called Pentagram map, which is a discretization of the Boussinesq dynamical system..

Esse trabalho visa a investigar a estrutura bi-Hamiltoniana de uma classe de sistemas dinâmicos. Depois de introduzir as ferramentas necessárias, a saber, as noções de variedade de Poisson, de grupo de PoissonLieedenetworknodiscoenoanêl,introduziremosossistemasdinâmicos relevantes nessa dissertação, chamados de reticulados de Coxeter-Toda. Esses sistemas dinâmicos, cujo espaço de fase pode ser identicado com umoportunoquocientedeumacéluladupladeCoxeter-Bruhatdogrupo linear geral, são obtidos por redução do sistema de Toda em GLn. Na parte nal do presente trabalho apresentaremos alguns resultados relacionado à um sistema dinâmico discreto chamado de aplicação do pentagrama, o qual pode ser obtido através uma oportuna discretização do sistema dinâmico de Boussinesq. / This work aims to study the bi-Hamiltonian structure of a class of dynamical systems. After introducing the relevant tools, namely the notions of Poisson manifold, Poisson-Lie group and of network dened in a disc and in an annulus, we will introduce the dynamical systems of interest for this dissertation, i.e., the Coxeter-Toda lattices. These dynamical systems, whose phase-space can be identied with a suitable quotient of a Coxeter double Bruhat cell of the general linear group, are obtained by reduction starting from the Toda ow on GLn. In the nal part of the present work will be presented some results concerning a discrete integrable system close to the so called Pentagram map, which is a discretization of the Boussinesq dynamical system..

A city is considered as a complex system. It consists of numerous interactivesub-systems and is affected by diverse factors including governmental landpolicies, population growth, transportation infrastructure, and market behavior.Land use and transportation systems are considered as the two most importantsubsystems determining urban form and structure in the long term. Meanwhile,urban growth is one of the most important topics in urban studies, and its maindriving forces are population growth and transportation development. Modelingand simulation are believed to be powerful tools to explore the mechanisms ofurban evolution and provide planning support in growth management. The overall objective of the thesis is to analyze and model urban growth basedon the simulation of land-use changes and the modeling of road networkexpansion. Since most previous urban growth models apply fixed transportnetworks, the evolution of road networks was particularly modeled. Besides,urban growth modeling is an interdisciplinary field, so this thesis made bigefforts to integrate knowledge and methods from other scientific and technicalareas to advance geographical information science, especially the aspects ofnetwork analysis and modeling. A multi-agent system was applied to model urban growth in Toronto whenpopulation growth is considered as being the main driving factor of urbangrowth. Agents were adopted to simulate different types of interactiveindividuals who promote urban expansion. The multi-agent model with spatiotemporalallocation criterions was shown effectiveness in simulation. Then, anurban growth model for long-term simulation was developed by integratingland-use development with procedural road network modeling. The dynamicidealized traffic flow estimated by the space syntax metric was not only used forselecting major roads, but also for calculating accessibility in land-usesimulation. The model was applied in the city centre of Stockholm andconfirmed the reciprocal influence between land use and street network duringthe long-term growth. To further study network growth modeling, a novel weighted network model,involving nonlinear growth and neighboring connections, was built from theperspective of promising complex networks. Both mathematical analysis andnumerical simulation were examined in the evolution process, and the effects ofneighboring connections were particular investigated to study the preferentialattachment mechanisms in the evolution. Since road network is a weightedplanar graph, the growth model for urban street networks was subsequentlymodeled. It succeeded in reproducing diverse patterns and each pattern wasexamined by a series of measures. The similarity between the properties of derived patterns and empirical studies implies that there is a universal growthmechanism in the evolution of urban morphology. To better understand the complicated relationship between land use and roadnetwork, centrality indices from different aspects were fully analyzed in a casestudy over Stockholm. The correlation coefficients between different land-usetypes and road network centralities suggest that various centrality indices,reflecting human activities in different ways, can capture land development andconsequently influence urban structure. The strength of this thesis lies in its interdisciplinary approaches to analyze andmodel urban growth. The integration of ‘bottom-up’ land-use simulation androad network growth model in urban growth simulation is the major contribution.The road network growth model in terms of complex network science is anothercontribution to advance spatial network modeling within the field of GIScience.The works in this thesis vary from a novel theoretical weighted network modelto the particular models of land use, urban street network and hybrid urbangrowth, and to the specific applications and statistical analysis in real cases.These models help to improve our understanding of urban growth phenomenaand urban morphological evolution through long-term simulations. Thesimulation results can further support urban planning and growth management.The study of hybrid models integrating methods and techniques frommultidisciplinary fields has attracted a lot attention and still needs constantefforts in near future. / <p>QC 20130514</p>